Project Euler Problem 40

Euler problem 40 can be solved quite easily using an intuitive brute force approach.
First we generate a string of the decimal fraction that is long enough to hold each of the requested digits. Then we read each digit and calculate the product. With getDecimalFraction and getDigit defined seperately this reduces to just a few lines of code:

int main() {
  int max = 6;
  string num = getDecimalFraction(pow(10,max));
  int product = 1;
  for (int i = 0; i <= max; i++) {
    int digit = getDigit(num, pow(10, i));
    cout << digit  << "  ";
    product *= digit;
  }
  cout << "\n" << product << endl;
  return 0;
}

The functions used in this snippet are defined like this:

// calculate decimal fraction by concatenating positive integers
// maxDigit is the maximum digit that needs to be contained;
// as soon as the length of the fraction is greater or equal
// to maxDigit the fraction is returned
std::string getDecimalFraction(int maxDigit) {
  std::string fraction = "";
  int i = 1;
  while(fraction.size() < maxDigit) {
    std::stringstream number;
    number << i;
    fraction += number.str();
    i++;
  }
  return fraction;
}

int getDigit(std::string fraction, int n) {
  if (n > fraction.size())
    throw std::exception();
  if (n < 1)
    throw std::exception();
  n--;
  int digit = (int) fraction[n] - '0';
  return digit;
}

You could also think of a solution by hand as there is a rule of how many digits you add with each integer (9 x 1 digit for 1...9, 990 x 2 digits for 10...999, etc.). However, the C++ solution is easy to implement and gives a fast answer to the question. As usual, the code can be found on github.